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  4. Current and resistance
  5. Resistivity and resistance

9.3 Resistivity and resistance  (Page 2/10)

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[1] Values depend strongly on amounts and types of impurities.
Resistivities and conductivities of various materials at 20 °c
Material Conductivity, σ
( Ω · m ) −1 		Resistivity, ρ
( Ω · m ) 		Temperature
Coefficient, α
( ° C ) −1
Conductors
Silver 6.29 × 10 7 1.59 × 10 −8 0.0038
Copper 5.95 × 10 7 1.68 × 10 −8 0.0039
Gold 4.10 × 10 7 2.44 × 10 −8 0.0034
Aluminum 3.77 × 10 7 2.65 × 10 −8 0.0039
Tungsten 1.79 × 10 7 5.60 × 10 −8 0.0045
Iron 1.03 × 10 7 9.71 × 10 −8 0.0065
Platinum 0.94 × 10 7 10.60 × 10 −8 0.0039
Steel 0.50 × 10 7 20.00 × 10 −8
Lead 0.45 × 10 7 22.00 × 10 −8
Manganin (Cu, Mn, Ni alloy) 0.21 × 10 7 48.20 × 10 −8 0.000002
Constantan (Cu, Ni alloy) 0.20 × 10 7 49.00 × 10 −8 0.00003
Mercury 0.10 × 10 7 98.00 × 10 −8 0.0009
Nichrome (Ni, Fe, Cr alloy) 0.10 × 10 7 100.00 × 10 −8 0.0004
Semiconductors [1]
Carbon (pure) 2.86 × 10 −6 3.50 × 10 −5 −0.0005
Carbon ( 2.86 − 1.67 ) × 10 −6 ( 3.5 − 60 ) × 10 −5 −0.0005
Germanium (pure) 600 × 10 −3 −0.048
Germanium ( 1 − 600 ) × 10 −3 −0.050
Silicon (pure) 2300 −0.075
Silicon 0.1 − 2300 −0.07
Insulators
Amber 2.00 × 10 −15 5 × 10 14
Glass 10 −9 − 10 −14 10 9 − 10 14
Lucite < 10 −13 > 10 13
Mica 10 −11 − 10 −15 10 11 − 10 15
Quartz (fused) 2.00 × 10 −15 75 × 10 16
Rubber (hard) 10 −13 − 10 −16 10 13 − 10 16
Sulfur 10 −15 10 15
Teflon TM < 10 −13 > 10 13
Wood 10 −8 − 10 −11 10 8 − 10 11

The materials listed in the table are separated into categories of conductors, semiconductors, and insulators, based on broad groupings of resistivity. Conductors have the smallest resistivity, and insulators have the largest; semiconductors have intermediate resistivity. Conductors have varying but large, free charge densities, whereas most charges in insulators are bound to atoms and are not free to move. Semiconductors are intermediate, having far fewer free charges than conductors, but having properties that make the number of free charges depend strongly on the type and amount of impurities in the semiconductor. These unique properties of semiconductors are put to use in modern electronics, as we will explore in later chapters.

Current density, resistance, and electrical field for a current-carrying wire

Calculate the current density, resistance, and electrical field of a 5-m length of copper wire with a diameter of 2.053 mm (12-gauge) carrying a current of I = 10 mA .

Strategy

We can calculate the current density by first finding the cross-sectional area of the wire, which is A = 3.31 mm 2 , and the definition of current density J = I A . The resistance can be found using the length of the wire L = 5.00 m , the area, and the resistivity of copper ρ = 1.68 × 10 −8 Ω · m , where R = ρ L A . The resistivity and current density can be used to find the electrical field.

Solution

First, we calculate the current density:

J = I A = 10 × 10 −3 A 3.31 × 10 −6 m 2 = 3.02 × 10 3 A m 2 .

The resistance of the wire is

R = ρ L A = ( 1.68 × 10 −8 Ω · m ) 5.00 m 3.31 × 10 −6 m 2 = 0.025 Ω .

Finally, we can find the electrical field:

E = ρ J = 1.68 × 10 −8 Ω · m ( 3.02 × 10 3 A m 2 ) = 5.07 × 10 −5 V m .

Significance

From these results, it is not surprising that copper is used for wires for carrying current because the resistance is quite small. Note that the current density and electrical field are independent of the length of the wire, but the voltage depends on the length.

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Check Your Understanding Copper wires use routinely used for extension cords and house wiring for several reasons. Copper has the highest electrical conductivity rating, and therefore the lowest resistivity rating, of all nonprecious metals. Also important is the tensile strength, where the tensile strength is a measure of the force required to pull an object to the point where it breaks. The tensile strength of a material is the maximum amount of tensile stress it can take before breaking. Copper has a high tensile strength, 2 × 10 8 N m 2 . A third important characteristic is ductility. Ductility is a measure of a material’s ability to be drawn into wires and a measure of the flexibility of the material, and copper has a high ductility. Summarizing, for a conductor to be a suitable candidate for making wire, there are at least three important characteristics: low resistivity, high tensile strength, and high ductility. What other materials are used for wiring and what are the advantages and disadvantages?

Silver, gold, and aluminum are all used for making wires. All four materials have a high conductivity, silver having the highest. All four can easily be drawn into wires and have a high tensile strength, though not as high as copper. The obvious disadvantage of gold and silver is the cost, but silver and gold wires are used for special applications, such as speaker wires. Gold does not oxidize, making better connections between components. Aluminum wires do have their drawbacks. Aluminum has a higher resistivity than copper, so a larger diameter is needed to match the resistance per length of copper wires, but aluminum is cheaper than copper, so this is not a major drawback. Aluminum wires do not have as high of a ductility and tensile strength as copper, but the ductility and tensile strength is within acceptable levels. There are a few concerns that must be addressed in using aluminum and care must be used when making connections. Aluminum has a higher rate of thermal expansion than copper, which can lead to loose connections and a possible fire hazard. The oxidation of aluminum does not conduct and can cause problems. Special techniques must be used when using aluminum wires and components, such as electrical outlets, must be designed to accept aluminum wires.

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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